cp's OEIS Frontend

A229430 Number of ways to label the cells of a 2 X n grid such that no (orthogonally) adjacent cells have adjacent labels.

%I A229430 #16 Feb 16 2025 08:33:20
%S A229430 1,0,0,24,1660,160524,21914632,4065598248,987830372684,
%T A229430 304870528356476,116578000930637000,54116343193686469960,
%U A229430 29984241542575292762940,19548555813018460134901516,14815308073366437897483622056,12915964646307201385492841052040
%N A229430 Number of ways to label the cells of a 2 X n grid such that no (orthogonally) adjacent cells have adjacent labels.
%C A229430 a(n) is the number of Hamiltonian paths in the complement of the n-ladder graph. - _Andrew Howroyd_, Feb 14 2020
%H A229430 Andrew Howroyd, <a href="/A229430/b229430.txt">Table of n, a(n) for n = 0..100</a>
%H A229430 F. C. Holroyd and W. J. G. Wingate, <a href="http://dx.doi.org/10.1016/S0012-365X(85)80003-0">Cycles in the complement of a tree or other graph</a>, Discrete Math., 55 (1985), 267-282.
%H A229430 Andrew Howroyd, <a href="/A229430/a229430.txt">Worked Solution and Formula</a>
%H A229430 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LadderGraph.html">Ladder Graph</a>
%H A229430 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a>
%e A229430 The A(3) = 24 valid labelings of a 2 X 3 grid are
%e A229430    153   163   135   513   415   416
%e A229430    426   425   462   246   263   253
%e A229430 together with their 18 reflections and rotations.
%o A229430 (PARI) seq(n)={my(gf=(1 - x)*(1 + (3*y - 2)*x + (y + 1)*x^2)/(1 + (-y^2 + 5*y - 3)*x + (y^3 - 3*y^2 + 3)*x^2 + (-2*y^3 + 5*y^2 - 3*y - 1)*x^3 + (y^3 - y^2 + 2*y)*x^4)); [subst(serlaplace(p*y^0),y,1) | p <- Vec(gf + O(x*x^n))]} \\ _Andrew Howroyd_, Feb 16 2020
%Y A229430 Row n=2 of A229429.
%Y A229430 Cf. A002464.
%K A229430 nonn
%O A229430 0,4
%A A229430 _Jens Voß_, Sep 23 2013
%E A229430 Terms a(9) and beyond from _Andrew Howroyd_, Feb 14 2020